Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2014; 51(4): 703-719

Printed July 1, 2014

https://doi.org/10.4134/JKMS.2014.51.4.703

Copyright © The Korean Mathematical Society.

Traveling wave solutions in nonlocal dispersal models with nonlocal delays

Shuxia Pan

Lanzhou University of Technology

Abstract

This paper is concerned with the traveling wave solutions of nonlocal dispersal models with nonlocal delays. The existence of traveling wave solutions is investigated by the upper and lower solutions, and the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate these results, a delayed competition model is considered by presenting the existence and nonexistence of traveling wave solutions, which completes and improves some known results. In particular, our conclusions can deal with the traveling wave solutions of evolutionary systems which admit large time delays reflecting intra-specific competition in population dynamics and leading to the failure of comparison principle in literature.

Keywords: upper-lower solutions, asymptotic spreading, contracting rectangle, large delay

MSC numbers: 35C07, 35K57, 37C65

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